NY airports remain closed, but Boston, Philly and D.C. are open*

Being open, however, doesn't necessarily mean that airlines will fly there. A carrier's route system relies on aircraft and personnel being available at a certain place at a certain time - and much of the Northeast, most especially NY's three main airports - remains out of commission. JFK's runways are flooded (they're all at or near sea level so you could imagine) and there are also electronic devices like runway lights that might have been damaged. From the SF Chronicle:

The situation remains fluid, and many airports could crank up again today, so here's the link to get current airport closure information. Looking at current flight boards, it appears that most early morning flights from SFO to Boston-Logan Airport, Washington-Dulles and Washington National were canceled, but flights later today are on schedule. Flights into New York appear to be cancelled all day. Some good news: While airlines cancelled some 7,000 flights yesterday and today, only about 600 are cancelled for tomorrow. So we are making some progress.

More than 300 flights in and out of LAX have been cancelled, with more expected today. Once flights resume, it will be many days before all the passengers on those flights can be re-booked. If that's not enough, the FAA suspended flights at the airport this morning due to heavy fog, but operations are back up.